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A116539
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Number of zero-one matrices with n ones and no zero rows or columns and with distinct rows, up to permutation of rows.
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28
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1, 1, 2, 7, 28, 134, 729, 4408, 29256, 210710, 1633107, 13528646, 119117240, 1109528752, 10889570768, 112226155225, 1210829041710, 13640416024410, 160069458445202, 1952602490538038, 24712910192430620, 323964329622503527, 4391974577299578248, 61488854148194151940
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OFFSET
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0,3
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COMMENTS
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Also the number of labeled hypergraphs spanning an initial interval of positive integers with edge-sizes summing to n. - Gus Wiseman, Dec 18 2018
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LINKS
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EXAMPLE
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The a(3) = 7 edge-sets:
{{1,2,3}}
{{1},{1,2}}
{{2},{1,2}}
{{1},{2,3}}
{{2},{1,3}}
{{3},{1,2}}
{{1},{2},{3}}
Inequivalent representatives of the a(4) = 28 0-1 matrices:
[1111]
.
[100][1000][010][0100][001][0010][0001][110][110][1100][101][1010][1001]
[111][0111][111][1011][111][1101][1110][101][011][0011][011][0101][0110]
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[10][100][100][1000][100][100][1000][1000][010][010][0100][0100][0010]
[01][010][010][0100][001][001][0010][0001][001][001][0010][0001][0001]
[11][101][011][0011][110][011][0101][0110][110][101][1001][1010][1100]
.
[1000]
[0100]
[0010]
[0001]
(End)
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MAPLE
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b:= proc(n, i, k) b(n, i, k):=`if`(n=0, 1, `if`(i<1, 0, add(b(n-i*j,
min(n-i*j, i-1), k)*binomial(binomial(k, i), j), j=0..n/i)))
end:
a:= n-> add(add(b(n$2, i)*(-1)^(k-i)*binomial(k, i), i=0..k), k=0..n):
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, Min[n - i*j, i - 1], k]*Binomial[Binomial[k, i], j], {j, 0, n/i}]]];
a[n_] := Sum[Sum[b[n, n, i]*(-1)^(k-i)*Binomial[k, i], {i, 0, k}], {k, 0, n}];
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CROSSREFS
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Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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